Electric field dependence of pocket and nonpocket impurity gap modes in KI and the establishment of Ag+ quadrupolar deformability.

Abstract

Far-infrared static electric field measurements have been made for a variety of KI point defects which produce vibrational modes in the pure crystal phonon gap. The extremely small field-induced frequency shifts (\ensuremath{\le}0.02 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) of the KI gap modes associated with anion impurities were accurately determined with a precision of \ifmmode\pm\else\textpm\fi{}0.003 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ by using a global analysis method. No frequency shifts were observed for the ${\mathrm{Rb}}^{+}$ or ${\mathrm{Cs}}^{+}$ gap modes, up to the maximum applied field of \ensuremath{\sim}100 kV/cm in the [100] direction. Most revealing are the field-induced frequency shifts for the pocket gap modes associated with the ${\mathrm{Ag}}^{+}$ impurity, which are nearly two orders of magnitude smaller than the field-induced shifts measured for low-frequency ${\mathrm{Ag}}^{+}$-induced resonant modes. The fact that the pocket-mode displacements are sharply peaked on the (200) family of ions renders them sensitive to the host-lattice anharmonicity near those sites, whereas the resonant modes probe the defect and its nearest neighbors. These E-field measurements and earlier stress-shift measurements are analyzed using a quasiharmonic perturbed shell model. In this approach the effect of either an applied stress or an applied E field is to move the equilibrium positions of the ions, thereby renormalizing the harmonic force constants via the local cubic and quartic anharmonicity.The two types of experiments produce local strains of orthogonal symmetries, and hence provide complementary information. The theoretical analysis of the E field and stress measurements allows us to establish firmly that the ${\mathrm{Ag}}^{+}$ ion in KI possesses a significant electronic quadrupolar deformability. In turn, this finding strongly supports earlier suggestions that the silver ion quadrupolar deformability is an important feature in the dynamics of other host-silver defect systems and of the silver halides. \textcopyright{} 1996 The American Physical Society.